Coalescent processes appear as the natural limits that describe
the genealogy of evolving population models. In fact, much of the research
on population models focuses on establishing this connection, often as weak limits under
appropriate time scales and/or time changes.
A primordial class of population models are Cannings' models [1]}, [2]}. These
are able to accommodate most biological premises that fall under
the assumption of neutral evolution. The key assumption of these models is that the offspring distribution of
the parents in any generation
should be exchangeable (invariant under permutations);
in particular all the parents have the same reproductive success, or fitness, in distribution.
Due to their wide applicability and manageability, Cannings' models
are among the most studied population evolution models.
The genealogy of Cannings' models was described in whole generality,
and in terms of coalescent processes, in the foundational work of [3]}.
After this, a wide literature was developed on the study of limit genealogies of evolution models.
Some are direct applications e.g. [4]}, or deal with a priori more complex models that can be reduced to Cannings' models e.g. [5]}, [6]}.
Others are modifications, such as models with varying population sizes [7]}, [8]}, [9]} or diploid reproduction [10]}, [11]}, using heuristics close to those of [3]}.
Finally some works use different techniques such as duality, e.g. in the case of populations suffering recurrent bottlenecks [13]} or overlapping generations [14]}.
